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Statement

There are $n$ lanterns arranged in a circle. Initially, these lanterns are all closed.

There are $n$ buttons on the console. Pressing the $x$th button will reverse the state of lantern $x$ and the two adjacent lanterns. "Reverse" means turning off to on, and turning on to off.

For example, if you press the $5$th button, lanterns $4$, $5$, and $6$ will all flip. If you press the $n$th button, the states of lanterns $n-1, n$ and $1$ will flip. This is because the lanterns are arranged in a ring, with $n-1$ and $1$ being adjacent to $n$.

We pressed some buttons one by one. You need to program to find the final state of the lanterns after our operation is completed.

Input

The first line contains two positive integers, $n$ and $m$,$(3\leq n,m\leq 10^5)$, representing the total number of lanterns, $n$, and the number of times we pressed the button, $m$.

The next $m$ lines each contain a positive integer, indicating which button we pressed during each operation.

Output

A single line of $n$ integers, separated by spaces, representing the states of $n$ lanterns. $0$ represents a lantern off, and $1$ represents a lantern on.

Samples

5 4
1 3 1 2

1 0 0 1 0

The status of the lantern sequence is as follows:

The final state of the lantern when pressing 2 is

So you should output 1 0 0 1 0